Human beings have long thought that planetary systems similar to our own should exist around stars other than the Sun. However, the astronomical search for planets outside our Solar System has had a dismal history of decades of discoveries that were announced, but could not be confirmed. All that changed in 1995, when we entered the era of the discovery of extrasolar planetary systems orbiting main-sequence stars. To date, well over 130 planets have been found outside our Solar System, ranging from the fairly familiar to the weirdly unexpected. Nearly all of the new planets discovered to date appear to be gas giant planets similar to our Jupiter and Saturn, though with very different orbits about their host stars. In the last year, three planets with much lower masses have been found, similar to those of Uranus and Neptune, but it is not yet clear if they are also ice giant planets, or perhaps rock giant planets, i.e., super-Earths. The long-term goal is to discover and characterize nearby Earth-like, habitable planets. A visionary array of space-based telescopes has been planned that will carry out this incredible search over the next several decades.